Question

Ln(2),ln(2) Evaluate log₅(100) using the change of base formula. sˡᵒᵍ⁵(100)=x⁵ 100=x⁵

Answer 1

To evaluate log5(100), use the change of base formula with base 10: log5(100) = log(100) / log(5), which gives approximately 2.8614.

Step-by-step explanation:

To evaluate log5(100) using the change of base formula, you can change the base to 10 or e (natural logarithm), for which calculators typically have built-in functions.

The change of base formula is given by:

logb(a) = logc(a) / logc(b), where c can be any positive number.

Using base 10, we get:

log5(100) = log10(100) / log10(5)

Since the common logarithm of 100 is 2 (because 102 = 100), and the common logarithm of 5 is approximately 0.69897 (because 100.69897 ≈ 5), we can substitute these values into the formula:

log5(100) = 2 / 0.69897 ≈ 2.8614

Therefore, log5(100) ≈ 2.8614.